St 16 starter Issue's??

Hi guy's I have been haveing trouble starting this tractor it seemed ok when we bought it the Prev. owner said that he had also had issue's so he tried a new starter and had the same issue so he ended up with bothe a new solinoid and starter. Well there is still some sort of issue?? The battery is new and reading over 12vdc while the engine is running it read's 13 plus? the ground is good? The only darn way we can get this sucker to run is to parallel a battery booster,then she will start but some times the thing need's a tap on the starter to get her to turn over? What the heck is up here?? Did these thing's have shims from the factory?This is drivingme nut's! Please help Lol!
Thanks

Could be the automatic compression release system is not working, raising the compression too high for the starter to overcome. 13+ volts running is correct. Needing to tap the starter sounds like the brushes are sticking in their slide. That or just real dirty inside the starter. This is a Tecumseh engine correct? I would look inside the starter, do whatever needed there, then see if the compression release is working. Most compression release systems are rendered useless if the valve clearances are too wide.